Multiple recurrence and hypercyclicity

2021/04/30 by Rodrigo Cardeccia, Cardeccia, Rodrigo, Santiago Muro +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2104.15033

openalex publication_date 2021/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study multiply recurrent and hypercyclic operators as a special case of \mathcal F-hypercyclicity, where \mathcal F is the family of subsets of the natural numbers containing arbitrarily long arithmetic progressions. We prove several properties of hypercyclic multiply recurrent operators, we characterize those operators which are weakly mixing and multiply recurrent, and we show that there are operators that are multiply recurrent and hypercyclic but not weakly mixing.

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